Xu Bian

Circuit Network Model of Stator Transposition Bar in Large Generators and Calculation of Circulating Current

Calculation of circulating current in transposition bars is important to the transposition-type design of stator windings in large generators. The circuit network model of the stator transposition bar, including only resistance and reactance parameters, is proposed in this paper, and the calculation method for parameters is given. The analytical algorithm of circulating current in stator transposition bars is proposed based on the circuit network model. Contrary to the existing calculation method for circulating current, the presented analytical algorithm is a general and fast method for different transposition types, which can avoid establishing complex 3-D models. In order to validate the proposed analytical algorithm, the strand current and circulating current of less than 540° with a void transposition bar in a water-cooled turbogenerator are calculated by analytical algorithm and 3-D finite-element method.

Analytic Algorithm for Strand Slot Leakage Reactance of the Transposition Bar in an AC Machine

Calculation of circulating current in transposition bars is the key problem in the design of stator windings, which will determine the transposition type of stator windings. The circuit equation method, in which the calculation of strand slot leakage reactance in transposition bars is the premise, is widely used in engineering to calculate circulating current. This paper describes an analytical algorithm for the calculation of strand slot leakage reactance in transposition bars called discrete integral method. The presented method is based on Amperes circuit law. The slot leakage reactance of strands in transposition bars is calculated by the integral of the transposition path discretized into many key points under the proper coordinate system. Contrary to the existing calculation formula, the discrete integral method is a general method for the calculation of slot leakage reactance, which can simulate the transposition path of different transposition types. In order to validate the discrete integral method, the circulating current generated by slot leakage magnetic field of two typical transposition bars is calculated by circuit equation method and finite-element method.

Finite-Element Calculation of 3-D Transient Electromagnetic Field in End Region and Eddy-Current Loss Decrease in Stator End Clamping Plate of Large Hydrogenerator

The stator clamping plate is an important component of hydrogenerators used to fasten the stator end core. Due to the complex leakage electromagnetic field in the end region, eddy-current loss in the stator clamping plate is usually very large, which will lead to partial overheat. Evaluation of eddy-current losses in stator clamping plates and reasonable structure design are the premise of ensuring the safe and stable operation of a large hydrogenerator. A 278-MVA hydrogenerator is taken as an example in this paper, and the calculation model of 3-D transient electromagnetic field of end region is established and validated by temperature test value. Then, a new arch-shaped clamping plate structure is presented. The transient electromagnetic field and eddy-current losses of end regions with traditional fan-shaped and new arch-shaped stator clamping plate structures are calculated by time-stepping finite-element method and are compared. Calculation results indicate that the new arch-shaped clamping plate structure can effectively reduce the eddy-current loss of stator clamping plate.

Analytical Algorithm for Strand End Leakage Reactance of Transposition Bar in AC Machine

Calculation of circulating current in transposition bars is the key problem in the design of stator windings, which will determine the transposition type of stator windings. The circuit equation method, in which the calculation of strand end leakage reactance in transposition bars is the premise, is widely used in engineering to calculate circulating current. This paper describes an analytical algorithm for the calculation of strand end leakage reactance in transposition bars, which is based on mirror image principle. The end leakage reactance of strands in transposition bar is calculated by the integral of transposition path discretized into many key points. Contrary to the existing calculation method, the analytical algorithm proposed in this paper is a general method for calculating the end leakage reactance, which can simulate the transposition path of strands in the end region for different transposition types. In order to validate the proposed method, the end coil self and mutual leakage reactance are calculated by proposed analytical algorithm and finite element method.

Influence of Void Transposition Structure on the Leakage Magnetic Field and Circulating Current Loss of Stator Bars in Water-Cooled Turbo-Generators

In the design of stator bar structure, void transposition is an important way of reducing circulating current loss in water-cooled turbo-generators. The different void transposition structures have a great influence on circulating current loss. However, the influences of void transposition structure on the leakage magnetic field and circulating current loss are not definite. A 600-MW water-cooled turbo-generator is taken as an example. A three-dimensional (3-D) physical model of transposition bars in a single slot is established, and the field-circuit coupling method is used in 3-D numerical calculation of the leakage magnetic field and circulating current loss. The influences of segment number and length of the void transposition on the slot leakage magnetic field, current, and circulating current loss are obtained. The relationship between the slot leakage magnetic field distribution along the axial direction and circulating current loss based on different void transposition structures is clarified. The numerical calculation accuracy is validated with the current test experiment. New strategies and theoretical basis will be provided for the optimal design and technology of the transposition bars.

Influence of material of rotor end plate on 3-D electromagnetic field and eddy current losses in end region of hydro-generator

In hydro-generator, rotor end plate is one of the most important components, which is usually placed in the space between pole and the end of field winding, used to clamp the laminated pole and prevent the damping ring from flying off because of large centrifugal force. Generally, rotor end plate is made of 1Crl8Ni9Ti, forged steel and cast steel, which are either non-magnetic or magnetic material. Magnetic characteristic of rotor end plate affects the distribution of end leakage magnetic field, and then affects eddy current losses of end structures. Therefore, it is necessary to research the influence of magnetic characteristic of rotor end plate on the electromagnetic field and eddy current losses of end structures. In the past, scholar paid more attention on the material of stator clamping plate and clamping finger [1], however, few people studied the influence of material of rotor end plate on electromagnetic field and eddy current losses in end region of hydro-generator. In this paper, a 250MW hydro-generator is taken as an example, physical and mathematical models of 3-D nonlinear transient electromagnetic field in end region are established. When non-magnetic and magnetic materials are adopted, transient electromagnetic field and eddy current losses of stator end structures are contrastively analyzed, which will provide useful reference for the reasonable design of end structures.

Analytical Algorithm of Calculating Circulating Currents Between the Strands of Stator Winding Bars of Large Turbo-Generators Considering the Air Gap Magnetic Field Entering Stator Slots

The accurate and fast calculation of circulating currents between strands for different transposition types is the important premise of the engineering design for stator bars in large turbo-generators. The air gap magnetic field partly enters into the stator slot, also generating circulating currents. However, there is a lack of fast simulation method for calculating the air gap magnetic field entering the stator slot in the existing calculation method for circulating currents. In this paper, the analytical algorithm of calculating circulating currents considering the air gap magnetic field entering stator slots is proposed, in which the equivalent circuit model of transposed strands in stator bars is established based on the superposition principle, the analytical algorithm of calculating the induced electromotive force is proposed based on the discrete integral method, and the analytical algorithm of calculating the air gap magnetic field entering stator slots is proposed based on the conformal mapping method. Then, a 1400-MW turbo-generator is taken as an example, circulating currents between transposed strands in stator bars under no-load and rated condition are calculated by the proposed analytical algorithm. Finally, the proposed analytical algorithm is validated by the two-dimensional finite element method.

The influence of transposition angle on three-dimensional global domain magnetic field of stator bar in water-cooled turbo-generator

In this paper, a 600 MW turbo-generator is used as an example. Three-dimensional (3-D) physical model of transposition bars in a single stator slot is established. Field-circuit coupling method is combined in 3-D numerical calculation. The influence of transposition angle on three-dimensional global domain magnetic field of stator bar in water-cooled turbo-generator is researched. The distribution changes of flux density, maximum current and circulating current loss in the corresponding transposition structure are obtained. New solution and theoretical basis will be provided for the structure optimization design of the stator bar.

Influence of slot radial magnetic field on circulating current in stator transposition strands of large turbogenerator

In large turbogenerators, the stator bars are made of several parallel strands which are connected together in end region. Because of the disparity of electromotive force between every two strands in the same bar, circulating current flows around a close-cycle and inevitably leads to useless circulating current losses, generating heat. Thus the transposition must be used in strands to avoid the circulating current, such as 540° transposition, void transposition, incomplete transposition, extended transposition, twin transposition bars and mixed transposition bars. How to ascertain the appropriate transposition type among so many transposition types depends on the calculation of circulating current.

The Influence of Transposition Angle on 3-D Global Domain Magnetic Field of Stator Bar in Water-Cooled Turbo-Generator

Reasonable transposition structure of stator bars in water-cooled turbo-generators could reduce circulating current of strands, and related factors on distribution change of circulating current are complex and diverse. Transposition angle is one of the most important influencing factors, and its influencing degree on circulating current is still unclear. A 600 MW water-cooled turbo-generator is set as an example, a 3-D physical model of transposition bars in a single slot is established, and a field-circuit coupling method is used in 3-D numerical calculation. The optimization of transposition angle is researched, and the distribution changes of 3-D global domain magnetic field, maximum current, and circulating current loss in different transposition angles are obtained. Finally, the calculation results are compared with that of the improved analytical algorithm to validate the accuracy of the solving model.